Simultaneous creatine and phosphocreatine mapping of skeletal muscle by CEST MRI at 3T.

PURPOSE: To confirm that CrCEST in muscle exhibits a slow-exchanging process, and to obtain high-resolution amide, creatine (Cr), and phosphocreatine (PCr) maps of skeletal muscle using a POlynomial and Lorentzian Line-shape Fitting (PLOF) CEST at 3T. METHODS: We used dynamic changes in PCr/CrCEST of mouse hindlimb before and after euthanasia to assign the Cr and PCr CEST peaks in the Z-spectrum at 3T and to obtain the optimum saturation parameters. Segmented 3D EPI was employed to obtain multi-slice amide, PCr, and Cr CEST maps of human skeletal muscle. Subsequently, the PCrCEST maps were calibrated using the PCr concentrations determined by 31 P MRS. RESULTS: A comparison of the Z-spectra in mouse hindlimb before and after euthanasia indicated that CrCEST is a slow-exchanging process in muscle (<150.7 s-1 ). This allowed us to simultaneously extract PCr/CrCEST signals at 3T using the PLOF method. We determined optimal B1 values ranging from 0.3 to 0.6 µT for CrCEST in muscle and 0.3-1.2 µT for PCrCEST. For the study on human calf muscle, we determined an optimum saturation time of 2 s for both PCr/CrCEST (B1 = 0.6 µT). The PCr/CrCEST using 3D EPI were found to be comparable to those obtained using turbo spin echo (TSE). (3D EPI/TSE PCr: (2.6 ± 0.3) %/(2.3 ± 0.1) %; Cr: (1.3 ± 0.1) %/(1.4 ± 0.07) %). CONCLUSIONS: Our study showed that in vivo CrCEST is a slow-exchanging process. Hence, amide, Cr, and PCr CEST in the skeletal muscle can be mapped simultaneously at 3T by PLOF CEST.

Whole-cerebrum guanidino and amide CEST mapping at 3 T by a 3D stack-of-spirals gradient echo acquisition.

PURPOSE: To develop a 3D, high-sensitivity CEST mapping technique based on the 3D stack-of-spirals (SOS) gradient echo readout, the proposed approach was compared with conventional acquisition techniques and evaluated for its efficacy in concurrently mapping of guanidino (Guan) and amide CEST in human brain at 3 T, leveraging the polynomial Lorentzian line-shape fitting (PLOF) method. METHODS: Saturation time and recovery delay were optimized to achieve maximum CEST time efficiency. The 3DSOS method was compared with segmented 3D EPI (3DEPI), turbo spin echo, and gradient- and spin-echo techniques. Image quality, temporal SNR (tSNR), and test-retest reliability were assessed. Maps of Guan and amide CEST derived from 3DSOS were demonstrated on a low-grade glioma patient. RESULTS: The optimized recovery delay/saturation time was determined to be 1.4/2 s for Guan and amide CEST. In addition to nearly doubling the slice number, the gradient echo techniques also outperformed spin echo sequences in tSNR: 3DEPI (193.8 ± 6.6), 3DSOS (173.9 ± 5.6), and GRASE (141.0 ± 2.7). 3DSOS, compared with 3DEPI, demonstrated comparable GuanCEST signal in gray matter (GM) (3DSOS: [2.14%-2.59%] vs. 3DEPI: [2.15%-2.61%]), and white matter (WM) (3DSOS: [1.49%-2.11%] vs. 3DEPI: [1.64%-2.09%]). 3DSOS also achieves significantly higher amideCEST in both GM (3DSOS: [2.29%-3.00%] vs. 3DEPI: [2.06%-2.92%]) and WM (3DSOS: [2.23%-2.66%] vs. 3DEPI: [1.95%-2.57%]). 3DSOS outperforms 3DEPI in terms of scan-rescan reliability (correlation coefficient: 3DSOS: 0.58-0.96 vs. 3DEPI: -0.02 to 0.75) and robustness to motion as well. CONCLUSION: The 3DSOS CEST technique shows promise for whole-cerebrum CEST imaging, offering uniform contrast and robustness against motion artifacts.

Creatine mapping of the brain at 3T by CEST MRI.

PURPOSE: To assess the feasibility of CEST-based creatine (Cr) mapping in brain at 3T using the guanidino (Guan) proton resonance. METHODS: Wild type and knockout mice with guanidinoacetate N-methyltransferase deficiency and low Cr and phosphocreatine (PCr) concentrations in the brain were used to assign the Cr and protein-based arginine contributions to the GuanCEST signal at 2.0 ppm. To quantify the Cr proton exchange rate, two-step Bloch-McConnell fitting was used to fit the extracted CrCEST line-shape and multi-B1 Z-spectral data. The pH response of GuanCEST was simulated to demonstrate its potential for pH mapping. RESULTS: Brain Z-spectra of wild type and guanidinoacetate N-methyltransferase deficiency mice show a clear Guan proton peak at 2.0 ppm at 3T. The CrCEST signal contributes ∼23% to the GuanCEST signal at B1 = 0.8 µT, where a maximum CrCEST effect of 0.007 was detected. An exchange rate range of 200-300 s-1 was estimated for the Cr Guan protons. As revealed by the simulation, an elevated GuanCEST in the brain is observed when B1 is less than 0.4 µT at 3T, when intracellular pH reduces by 0.2. Conversely, the GuanCEST decreases when B1 is greater than 0.4 µT with the same pH drop. CONCLUSIONS: CrCEST mapping is possible at 3T, which has potential for detecting intracellular pH and Cr concentration in brain.

Uncertainty quantification for the random HIV dynamical model driven by drug adherence.

In HIV drug therapy, the high variability of CD4+ T cells and viral loads brings uncertainty to the determination of treatment options and the ultimate treatment efficacy, which may be the result of poor drug adherence. We develop a dynamical HIV model coupled with pharmacokinetics, driven by drug adherence as a random variable, and systematically study the uncertainty quantification, aiming to construct the relationship between drug adherence and therapeutic effect. Using adaptive generalized polynomial chaos, stochastic solutions are approximated as polynomials of input random parameters. Numerical simulations show that results obtained by this method are in good agreement, compared with results obtained through Monte Carlo sampling, which helps to verify the accuracy of approximation. Based on these expansions, we calculate the time-dependent probability density functions of this system theoretically and numerically. To verify the applicability of this model, we fit clinical data of four HIV patients, and the goodness of fit results demonstrate that the proposed random model depicts the dynamics of HIV well. Sensitivity analyses based on the Sobol index indicate that the randomness of drug effect has the greatest impact on both CD4+ T cells and viral loads, compared to random initial values, which further highlights the significance of drug adherence. The proposed models and qualitative analysis results, along with monitoring CD4+ T cells counts and viral loads, evaluate the influence of drug adherence on HIV treatment, which helps to better interpret clinical data with fluctuations and makes several contributions to the design of individual-based optimal antiretroviral strategies.

Technical variability of cornea parameters derived from anterior segment OCT fitted with Fringe Zernike polynomials.

BACKGROUND: This study uses bootstrapping to evaluate the technical variability (in terms of model parameter variation) of Zernike corneal surface fit parameters based on Casia2 biometric data. METHODS: Using a dataset containing N = 6953 Casia2 biometric measurements from a cataractous population, a Fringe Zernike polynomial surface of radial degree 10 (36 components) was fitted to the height data. The fit error (height - reconstruction) was bootstrapped 100 times after normalisation. After reversal of normalisation, the bootstrapped fit errors were added to the reconstructed height, and characteristic surface parameters (flat/steep axis, radii, and asphericities in both axes) extracted. The median parameters refer to a robust surface representation for later estimates of elevation, whereas the SD of the 100 bootstraps refers to the variability of the surface fit. RESULTS: Bootstrapping gave median radius and asphericity values of 7.74/7.68 mm and -0.20/-0.24 for the corneal front surface in the flat/steep meridian and 6.52/6.37 mm and -0.22/-0.31 for the corneal back surface. The respective SD values for the 100 bootstraps were 0.0032/0.0028 mm and 0.0093/0.0082 for the front and 0.0126/0.0115 mm and 0.0366/0.0312 for the back surface. The uncertainties for the back surface are systematically larger as compared to the uncertainties of the front surface. CONCLUSION: As measured with the Casia2 tomographer, the fit parameters for the corneal back surface exhibit a larger degree of variability compared with those for the front surface. Further studies are needed to show whether these uncertainties are representative for the situation where actual repeat measurements are possible.

Mixed uncertainty analysis on pumping by peristaltic hearts using Dempster-Shafer theory.

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster-Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief functions. With three representative probability distributions consistent with the belief structure, global sensitivity analysis has also been implemented to identify important uncertain factors and the results have been compared between different peristalsis models. To reduce the computational cost, physics constrained generalized polynomial chaos method is adopted to construct cheaper surrogates as approximations for the full simulation.

Simultaneous analysis of shape and internal structure of a curved Hibiscus cannabinus pulvinus: X-ray microtomography and semi-automated quantification.

In the Malvaceae family, dynamic solar tracking by leaves is actuated by the deformation of the pulvinus, a thickened region at the leaf blade-petiole junction. While the internal structure is believed to play a crucial role in this process, experimental verification has been challenging due to technical limitations. To address this gap, we developed a semi-automated workflow, which integrates data analysis and image processing to simultaneously analyze the shape and internal structure of a Malvaceae pulvinus using X-ray microtomography. Firstly, we found that kenaf (Hibiscus cannabinus L.), a Malvaceae species with curved pulvini, exhibited solar-tracking leaf movement and selected it as a model system. We employed diffusible iodine-based contrast-enhanced computed tomography to visualize the internal structure of the kenaf pulvinus. Analysis of the pulvini's shape revealed variations in pulvinus morphology, yet plausible prediction of the centerline was accomplished using polar polynomial regression. Upon slicing the pulvini perpendicular to the centerline, we observed distinct gray value gradients along the proximo-distal and adaxial-abaxial axes, challenging threshold-based tissue segmentation. This workflow successfully generated three modified 3D images and derived quantitative parameters. Using these quantitative parameters, we conducted network analysis and found the linkage between the size-normalized cortex cross-sectional area and curvature. Polynomial least absolute shrinkage and selection operator (LASSO) regression revealed the relationship between the size-normalized cortex cross-sectional area and curvature commonly in all three tested samples. This workflow enables simultaneous analysis of the shape and internal structure, significantly improving the reproducibility of Malvaceae leaf pulvinus characterization.

Modelling the lactation curve in Alpine × Beetal crossbred dairy goats using random regression models fitted with Legendre polynomial and B-spline functions.

The current study sought to genetically assess the lactation curve of Alpine × Beetal crossbred goats through the application of random regression models (RRM). The objective was to estimate genetic parameters of the first lactation test-day milk yield (TDMY) for devising a practical breeding strategy within the nucleus breeding programme. In order to model variations in lactation curves, 25,998 TDMY records were used in this study. For the purpose of estimating genetic parameters, orthogonal Legendre polynomials (LEG) and B-splines (BS) were examined in order to generate suitable and parsimonious models. A single-trait RRM technique was used for the analysis. The average first lactation TDMY was 1.22 ± 0.03 kg and peak yield (1.35 ± 0.02 kg) was achieved around the 7th test day (TD). The present investigation has demonstrated the superiority of the B-spline model for the genetic evaluation of Alpine × Beetal dairy goats. The optimal random regression model was identified as a quadratic B-spline function, characterized by six knots to represent the central trend. This model effectively captured the patterns of additive genetic influences, animal-specific permanent environmental effects (c2) and 22 distinct classes of (heterogeneous) residual variance. Additive variances and heritability (h2) estimates were lower in the early lactation, however, moderate across most parts of the lactation studied, ranging from 0.09 ± 0.04 to 0.33 ± 0.06. The moderate heritability estimates indicate the potential for selection using favourable combinations of test days throughout the lactation period. It was also observed that a high proportion of total variance was attributed to the animal's permanent environment. Positive genetic correlations were observed for adjacent TDMY values, while the correlations became less pronounced for more distant TDMY values. Considering better fitting of the lactation curve, the use of B-spline functions for genetic evaluation of Alpine × Beetal goats using RRM is recommended.

Optimal Piecewise Polynomial Approximation for Minimum Computing Cost by Using Constrained Least Squares.

In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares. In time-sensitive applications or in embedded systems with limited resources, the runtime of the approximate function is as crucial as its accuracy. The proposed algorithm searches for the optimal piecewise polynomial (OPP) with the minimum computational cost while ensuring that the error is below a specified threshold. This was accomplished by using smooth piecewise polynomials with optimal order and numbers of intervals. The computational cost only depended on polynomial complexity, i.e., the order and the number of intervals at runtime function call. In previous studies, the user had to decide one or all of the orders and the number of intervals. In contrast, the OPP approximation algorithm determines both of them. For the optimal approximation, computational costs for all the possible combinations of piecewise polynomials were calculated and tabulated in ascending order for the specific target CPU off-line. Each combination was optimized through constrained least squares and the random selection method for the given sample points. Afterward, whether the approximation error was below the predetermined value was examined. When the error was permissible, the combination was selected as the optimal approximation, or the next combination was examined. To verify the performance, several representative functions were examined and analyzed.

Using Diffraction Deep Neural Networks for Indirect Phase Recovery Based on Zernike Polynomials.

The phase recovery module is dedicated to acquiring phase distribution information within imaging systems, enabling the monitoring and adjustment of a system's performance. Traditional phase inversion techniques exhibit limitations, such as the speed of the sensor and complexity of the system. Therefore, we propose an indirect phase retrieval approach based on a diffraction neural network. By utilizing non-source diffraction through multiple layers of diffraction units, this approach reconstructs coefficients based on Zernike polynomials from incident beams with distorted phases, thereby indirectly synthesizing interference phases. Through network training and simulation testing, we validate the effectiveness of this approach, showcasing the trained network's capacity for single-order phase recognition and multi-order composite phase inversion. We conduct an analysis of the network's generalization and evaluate the impact of the network depth on the restoration accuracy. The test results reveal an average root mean square error of 0.086λ for phase inversion. This research provides new insights and methodologies for the development of the phase recovery component in adaptive optics systems.

A Two-Step Regional Ionospheric Modeling Approach for PPP-RTK.

In the precise point positioning/real-time kinematic (PPP-RTK) technique, high-precision ionospheric delay correction information is an important prerequisite for rapid PPP convergence. The commonly used ionospheric modeling approaches in the PPP-RTKs only take the trend term of the ionospheric total electron content (TEC) variations into account. As a result, the residual ionospheric delay still affects the positioning solutions. In this study, we propose a two-step regional ionospheric modeling approach that involves combining a polynomial fitting model (PFM) and a Kriging interpolation (KI) model. In the first step, a polynomial fitting method is used to model the trend term of the ionospheric TEC variations. In the second step, a KI method is used to compensate for the residual term of the ionospheric TEC variations. Datasets collected from continuously operating reference stations (CORSs) in Hunan Province, China, are used to validate the PFM/KI method by comparing with a single PFM method and a combined PFM and inverse distance weighting interpolation (IDWI) method. The experimental results show that the two-step PFM/KI modeled ionospheric delay achieves an average root mean square (RMS) error of 1.8 cm, which is improved by about 48% and 23% when compared with the PFM and PFM/IDWI methods, respectively. Regarding the positioning performance, the PPP-RTK with the PFM/KI method takes an average of 1.8 min or 4.0 min to converge to a positioning accuracy of 1.3 cm or 2.5 cm in the horizontal and vertical directions, respectively. The convergence times are decreased by about 18% and 14% in the horizontal direction and 9% and 5% in the vertical direction over the PFM and the PFM/IDWI methods, respectively.

Exploring Wavefront Detection in Imaging Systems with Rectangular Apertures Using Phase Diversity.

The attainment of a substantial aperture in the rotating synthetic aperture imaging system involves the rotation of a slender rectangular primary mirror. This constitutes a pivotal avenue of exploration in space telescope research. Due to the considerable aspect ratio of the primary mirror, environmental disturbances can significantly impact its surface shape. Active optical technology can rectify surface shape irregularities through the detection of wavefront information. The Phase Diversity (PD) method utilizes images captured by the imaging system to compute wavefront information. In this study, the PD method is applied to rotating synthetic and other rectangular aperture imaging systems, employing Legendre polynomials to model the wavefront. The study delved into the ramifications stemming from the aperture aspect ratio and aberration size.

Research on Decoupling Model of Six-Component Force Sensor Based on Artificial Neural Network and Polynomial Regression.

A two-stage decoupling model based on an artificial neural network with polynomial regression is proposed for the six-component force sensor load decoupling problem in the case of multidimensional mixed loading. The six-dimensional load categorization stage model constructed in the first stage combines 63 load category label sets with a deep BP neural network. The six-dimensional load regression stage model was constructed by combining polynomial regression with a BP neural network in the second stage. Meanwhile, the six-component force sensor with a fiber Bragg grating (FBG) sensor as the sensitive element was designed, and the elastomer simulation and calibration experimental dataset was established to realize the validation of the two-stage decoupling model. The results based on the simulation data show that the accuracy of the classification stage is 93.65%. The MAPE for the force channel in the regression stage is 6.29%, and 3.24% for the moment channel. The results based on experimental data show that the accuracy of the classification stage is 87.80%. The MAPE for the force channel in the regression phase is 5.63%, and 4.82% for the moment channel.

Research on Lane-Changing Decision Making and Planning of Autonomous Vehicles Based on GCN and Multi-Segment Polynomial Curve Optimization.

This paper considers the interactive effects between the ego vehicle and other vehicles in a dynamic driving environment and proposes an autonomous vehicle lane-changing behavior decision-making and trajectory planning method based on graph convolutional networks (GCNs) and multi-segment polynomial curve optimization. Firstly, hierarchical modeling is applied to the dynamic driving environment, aggregating the dynamic interaction information of driving scenes in the form of graph-structured data. Graph convolutional neural networks are employed to process interaction information and generate ego vehicle's driving behavior decision commands. Subsequently, collision-free drivable areas are constructed based on the dynamic driving scene information. An optimization-based multi-segment polynomial curve trajectory planning method is employed to solve the optimization model, obtaining collision-free motion trajectories satisfying dynamic constraints and efficiently completing the lane-changing behavior of the vehicle. Finally, simulation and on-road vehicle experiments are conducted for the proposed method. The experimental results demonstrate that the proposed method outperforms traditional decision-making and planning methods, exhibiting good robustness, real-time performance, and strong scenario generalization capabilities.

A Novel Piecewise Cubic Hermite Interpolating Polynomial-Enhanced Convolutional Gated Recurrent Method under Multiple Sensor Feature Fusion for Tool Wear Prediction.

The monitoring of the lifetime of cutting tools often faces problems such as life data loss, drift, and distortion. The prediction of the lifetime in this situation is greatly compromised with respect to the accuracy. The recent rise of deep learning, such as Gated Recurrent Unit Units (GRUs), Hidden Markov Models (HMMs), Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Attention networks, and Transformers, has dramatically improved the data problems in tool lifetime prediction, substantially enhancing the accuracy of tool wear prediction. In this paper, we introduce a novel approach known as PCHIP-Enhanced ConvGRU (PECG), which leverages multiple-feature fusion for tool wear prediction. When compared to traditional models such as CNNs, the CNN Block, and GRUs, our method consistently outperformed them across all key performance metrics, with a primary focus on the accuracy. PECG addresses the challenge of missing tool wear measurement data in relation to sensor data. By employing PCHIP interpolation to fill in the gaps in the wear values, we have developed a model that combines the strengths of both CNNs and GRUs with data augmentation. The experimental results demonstrate that our proposed method achieved an exceptional relative accuracy of 0.8522, while also exhibiting a Pearson's Correlation Coefficient (PCC) exceeding 0.95. This innovative approach not only predicts tool wear with remarkable precision, but also offers enhanced stability.

Calibration of Dual-Channel Raman Spectrometer via Optical Frequency Comb.

The portable Raman spectrometer boasts portability, rapid analysis, and high flexibility. It stands as a crucial and powerful technical tool for analyzing the chemical composition of samples, whether biological or non-biological, across diverse fields. To improve the resolution of grating spectrometers and ensure a wide spectral range, many spectrometer systems have been designed with double-grating structures. However, the impact of external forces, such as installation deviations and inevitable collisions, may cause differences between the actual state of the internal spectrometer components and their theoretical values. Therefore, spectrometers must be calibrated to establish the relationship between the wavelength and the pixel positions. The characteristic peaks of commonly used calibration substances are primarily distributed in the 200-2000 cm-1 range. The distribution of characteristic peaks in other wavenumber ranges is sparse, especially for spectrometers with double-channel spectral structures and wide spectral ranges. This uneven distribution of spectral peaks generates significant errors in the polynomial fitting results used to calibrate spectrometers. Therefore, to satisfy the calibration requirements of a dual-channel portable Raman spectrometer with a wide spectral range, this study designed a calibration method based on an optical frequency comb, which generates dense and uniform comb-like spectral signals at equal intervals. The method was verified experimentally and compared to the traditional calibration method of using a mercury-argon lamp. The results showed that the error bandwidth of the calibration results of the proposed method was significantly smaller than that of the mercury-argon lamp method, thus demonstrating a substantial improvement in the calibration accuracy.

Trade-offs of praise and criticism: Parents' responses to children's performance and children's resilience and depression.

In contrast to cognitive outcomes, parental success-oriented responses to children's performance enhanced the emotional well-being of children. Conversely, parental failure-oriented responses had the opposite impact. Thus, it remains unclear which response or combination of responses parents should employ to maximize their children's development. This research aimed to examine the combined effect of children's perceptions of parental success- and failure-oriented responses on children's depression, with a focus on the mediating role of resilience. A total of 651 pupils (44.7% female, Mage = 10.31, range = 8-12) were investigated in China using polynomial regression and response surface analyses. Our findings suggest that when success- and failure-oriented responses are congruent, failure-oriented responses counteract the protective effect of success-oriented responses against children's depression. The two equally matched responses demonstrated a curvilinear main effect on resilience, indicating that higher resilience was associated with the upper-middle range of the two responses. Moreover, children who reported more success-oriented responses than failure-oriented responses showed greater resilience and decreased depression. Resilience acted as a mediator for the combined effects of parental success and failure-oriented responses on children's depression. The study addressed the parenting dilemma, specifically the trade-off between success- and failure-oriented responses in promoting children's optimal development.

Trust (in)congruence, open innovation, and circular economy performance: Polynomial regression and response surface analyses.

Engaging partner firms in open innovation is critical to overcoming internal resource/capability constraints to achieve firm and supply chain circular economy (CE) performance, yet scholars have not examined this link empirically. Further, while researchers have repeatedly emphasized trust as a key driver of open innovation performance, little is known from a dyadic trust perspective (e.g., congruence vs. incongruence, high-high congruence vs. low-low congruence). To fill these gaps, we propose a theoretical model based on the social exchange theory (SET) and test it using a dyadic dataset of listed Chinese manufacturing firms. The results suggest that 1) rather than unilateral trust from the focal firm or its partners, trust congruence is more predictive of successful open process and product innovations, 2) regarding congruence types (low-low vs. high-high), congruence at higher levels of trust facilitates open product innovation more than low-low trust congruence; interestingly, such an effect is not significant for open process innovation, 3) open process innovation has a positive influence on the focal firm's CE performance, but its impact on supply chain CE performance is not statistically significant, and 4) open product innovation has a significantly positive impact on the focal firm and supply chain CE performance. Our findings still hold after analyzing time-lagged models and alternative measurements as robustness checks. Our study provides meaningful theoretical contributions to the literature and useful, practical insights for managing inter-organizational relationships, open innovation, and CE performance.

Theory of Mind and Social Informant Discrepancy in Autism.

When autistic youth are asked to assess their own social skills, they frequently rate themselves more favorably than their parents rate them. The magnitude of this informant discrepancy has been shown to relate to key clinical outcomes such as treatment response. It has been proposed that this discrepancy arises from difficulties with Theory of Mind. Participants were 167 youth 11 to 17 years old; 72% male, and their parents. Youth completed self-report measures of social skills and social cognitive tasks, while their parents completed questionnaires regarding social skills. A repeated-measures ANOVA indicated both non-autistic and autistic youth rated themselves more favorably than their parents rated them across all measures. Zero-order correlations revealed that raw differences between parent- and participant-report were negatively correlated with scores on parent-reported Theory of Mind measures. However, polynomial analysis did not indicate interaction effects between parent- and participant-report on any of the measures used. Polynomial regression revealed that increases in parent-reported social skill predicted larger increases in parent-report Theory of Mind at low levels of parent-reported social skill compared to high levels of parent-reported social skill. Participant-report social skills predicted performance on a behavioral Theory of Mind test in a curvilinear fashion, such that the relationship was positive at low levels of participant-reported social skills, but negative at high levels. This study replicates the finding that raw difference score analyses may result in illusory effects that are not supported when using more contemporary analysis methods, and that more complex and subtle relationships between social insight and perspective-taking exist within autistic youth.

Experimental validation off-line a nonlinear controller for removal of chromium using non-living cells of Yarrowia lipolytica.

The removal of hexavalent chromium [Cr (VI)] using non-living cells of Yarrowia lipolytica was investigated. Batch and continuous studies on removal of Cr (VI) achieved 97% and 99% removal from aqueous phase, respectively. The specific uptake values at pH of 2 in batch process were 40.73 ± 1.3 mg/g and 30.09 ± 0.23 mg/g on non-living cells, when 100 and 200 mg/L of metal Cr (VI) concentrations were used. In order to investigate the regulation of Cr (VI) under continuous operation based on reaction volume numerically a new class of feedback controller from structure polynomial was designed. The proposed methodology was used to an experimentally kinetic model for a removal Cr (VI) from Yarrowia lipolytica biomass was showed satisfactory closed-loop performance the proposed controller. Starting from an off-line optimization performed in simulation, we present the controller implementation, focussing on the methodology required to could be suitable for implementation in real time. In our experimental results, we highlight some discrepancies between simulation and reality despite these differences, the controller managed to perform convergence to removal Cr (VI). Finally, the results validated with off-line samples suggest that the proposed control could be suitable for in application in potential scenarios for wastewater treatment.